I have a GMS 1.2 engine and have experienced the same problems you have posted. I will suggest a possible fix to your problem.
Turn the low speed needle valve in until it bottoms out. Backout 2.5 turns. This setting will become your starting point for adjusting the low end. You may want to call this the factory setting.
Go to full throttle addjust for maximum RPM and backoff and 1/8 to 1/4 turn. Now go to the desired low throttle rpm you wish to run. This will depend on the propellor diameter and pitch. Smoothly and slowly advance the throttle. Note how the engine sounds and behaves. If the setting is too rich it will start to hesitate and if it is too lean it will most likely die.
Adjust the low end needle valve to retify these problems. It may work, mine did.